A family of iterative methods with sixth and seventh order convergence for nonlinear equations

DOI10.1016/j.mcm.2010.05.033zbMath1205.65170OpenAlexW2027649354MaRDI QIDQ623050

José L. Hueso, Alicia Cordero, Eulalia Martínez, Juan Ramón Torregrosa Sánchez

Publication date: 13 February 2011

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2010.05.033

zbMATH Keywords

iterative methodsnonlinear equationslinear interpolationdivided differencesconvergence orderefficiency index

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (13)

Complex dynamics of a sixth and seventh order family of root finding methods ⋮ An optimal and efficient general eighth-order derivative free scheme for simple roots ⋮ Numerical solution of nonlinear equations by an optimal eighth-order class of iterative methods ⋮ A new family of optimal eighth order methods with dynamics for nonlinear equations ⋮ Higher order methods for nonlinear equations and their basins of attraction ⋮ Extended local convergence for some inexact methods with applications ⋮ Two optimal general classes of iterative methods with eighth-order ⋮ Regarding the accuracy of optimal eighth-order methods ⋮ A new general eighth-order family of iterative methods for solving nonlinear equations ⋮ Local Convergence of a Family of Iterative Methods with Sixth and Seventh Order Convergence Under Weak Conditions ⋮ Efficacy of optimal methods for nonlinear equations with chemical engineering applications ⋮ Efficient Ostrowski-like methods of optimal eighth and sixteenth order convergence and their dynamics ⋮ An efficient family of weighted-Newton methods with optimal eighth order convergence

Cites Work

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• Three-step iterative methods with eighth-order convergence for solving nonlinear equations
• Two new families of sixth-order methods for solving nonlinear equations
• Some modifications of Newton's method with fifth-order convergence
• Some variants of Ostrowski's method with seventh-order convergence
• A sixth order method for nonlinear equations
• A variant of Newton's method with accelerated third-order convergence

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